The formula triangle
Speed, distance and time are linked by one relationship:
Speed = Distance ÷ Time
Rearranged:
- Distance = Speed × Time
- Time = Distance ÷ Speed
A memory trick is the triangle with D on top and S and T on the bottom. Cover the one you want: D = S × T; S = D/T; T = D/S.
Units
| Distance | Time | Speed unit |
|---|---|---|
| kilometres | hours | km/h |
| metres | seconds | m/s |
| miles | hours | mph |
Units must match. If speed is in km/h, time must be in hours.
Examples
Find speed: A train travels 360 km in 4 hours.
S = 360 ÷ 4 = 90 km/h
Find distance: A cyclist rides at 18 km/h for 2.5 hours.
D = 18 × 2.5 = 45 km
Find time: A car travels 210 km at 70 km/h.
T = 210 ÷ 70 = 3 hours
Converting minutes to hours
Divide minutes by 60.
- 30 min = 0.5 h
- 45 min = 0.75 h
- 20 min = 1/3 h
Example: Walking at 5 km/h for 36 minutes: 36 min = 0.6 h → D = 5 × 0.6 = 3 km.
Converting between km/h and m/s
- km/h → m/s: divide by 3.6
- m/s → km/h: multiply by 3.6
A sprinter running 10 m/s is going 36 km/h.
Average speed
Average speed = total distance ÷ total time (not the average of the speeds!).
Example: You drive 120 km at 60 km/h (2 h) and then 120 km at 120 km/h (1 h).
Average speed = 240 km ÷ 3 h = 80 km/h, not 90 km/h.
Distance–time graphs
On a distance–time graph, a steeper line means faster speed. A flat line means stopped.
Worked examples
Example 1: A plane flies 2,100 km in 2.5 h. Speed?
840 km/h.
Example 2: How long to walk 7.5 km at 5 km/h?
1.5 h (1 h 30 min).
Example 3: A car goes 50 km in 40 min. Speed in km/h?
40 min = 2/3 h → 50 ÷ (2/3) = 75 km/h.
Common mistakes
- Mixing minutes and hours.
- Writing 1.5 h as 1 h 50 min. It’s 1 h 30 min.
- Averaging speeds instead of using total distance ÷ total time.
Try it yourself
- 150 km in 2 h. Speed?
- 65 km/h for 3 h. Distance?
- 400 km at 80 km/h. Time?
- 12 km in 45 min. Speed in km/h?
- Convert 25 m/s to km/h.
Answers: 1) 75 km/h 2) 195 km 3) 5 h 4) 16 km/h 5) 90 km/h
Quick recap
- Speed = distance ÷ time.
- Keep units consistent; convert minutes to hours.
- Average speed = total distance ÷ total time.